Logic and Philosophy of Science Group Talk (Andrew Y. Lee, Toronto)

The Logic and Philosophy of Science Group is pleased to welcome as guest speaker Andrew Y. Lee, an assistant professor in the Department of Philosophy at the University of Toronto. Dr. Lee is interested in the structure of consciousness. His work examines how structural concepts—such as degrees, dimensions, continuity, discreteness, parts, wholes, isomorphisms, and state-spaces—can be applied to conscious experiences. Some of his work can be described as “mathematical phenomenology.”

This will be a discussion of recent work, to be circulated in advance. Please get in touch with Denis Walsh to receive a copy.

Talk Title

A Puzzle about Sums

Talk Abstract

A famous mathematical theorem says that the sum of an infinite series of numbers can depend on the order in which those numbers occur. Suppose we interpret the numbers in such a series as representing instances of some physical quantity, such as the weights of a collection of items. The mathematics seems to lead to the result that the weight of a collection of items can depend on the order in which those items are weighed. But that is very hard to believe! A puzzle then arises: How do we interpret the metaphysical significance of this mathematical theorem? I first argue that prior solutions to the puzzle lead to implausible consequences. Then I develop my own solution, where the basic idea is that the weight of a collection of items is equal to the limit of the weights of its finite subcollections contained within ever-expanding regions of space. I show how my solution is intuitively plausible and philosophically motivated, how it reveals an underexplored line of metaphysical inquiry about quantities and locations, and how it elucidates some classic puzzles concerning supertasks.

Note

I’m working on a new philosophical puzzle—about Hotel infinity—that’s closely related to the subject-matter of this paper. I’ll start the session by briefly presenting the new puzzle, and then open up discussion on either “A Puzzle about Sums” or on the new puzzle.

About the Logic and Philosophy of Science Group

One of six departmental Research Interest Groups, the Logic and Philosophy of Science Group hosts talks on logic, general philosophy of science, and philosophy of the particular sciences, as well as talks in allied areas such as formal epistemology, decision theory, and the metaphysics of science.